29:null 2a:["$","title",null,{"children":"DDD#8 An illusion of predictability | Lao | Observable"}] 2f:T519,arg = { let u = 0 // mean let s = 1 // standard deviation let a = 2 // left shape constant let b = 4 // right shape constant let c = 3 // middle shape constant let k = 2 // general shape parameter let l = 1 // exponential constant let d1 = 10, d2 = 20 // degrees of freedom let p = .08 // success probability return [ ({arg: [a,b], name: "arcsine"}), ({arg: [a,b], name: "beta"}), ({arg: [a,b], name: "betaprime"}), //({arg: [u,k], name: "cauchy"}), ({arg: [d1], name: "chi"}), ({arg: [d1], name: "chisquare"}), ({arg: [u,s], name: "cosine"}), ({arg: [k,l], name: "erlang"}), ({arg: [l], name: "exponential"}), ({arg: [d1,d2], name: "f"}), ({arg: [a,s, u], name: "frechet"}), ({arg: [a,b], name: "gamma"}), ({arg: [u,b], name: "gumbel"}), ({arg: [a,b], name: "invgamma"}), ({arg: [a,b], name: "kumaraswamy"}), ({arg: [u,b], name: "laplace"}), ({arg: [u,c], name: "levy"}), ({arg: [u,s], name: "logistic"}), ({arg: [u,s], name: "lognormal"}), ({arg: [u,s], name: "normal"}), ({arg: [a,b], name: "pareto1"}), ({arg: [s], name: "rayleigh"}), ({arg: [d1], name: "t"}), ({arg: [a,b,c], name: "triangular"}), ({arg: [-s,s], name: "uniform"}), ({arg: [k,l], name: "weibull"}), ] }30:T5a1,{ let dataFunction = [] let dataMean = [] let dataText = [] let n = 1000 let s = 1 let parameters = arg.find( e=> e.name == type ).arg let noMean = ['cauchy'] let mean = noMean.includes(type) ? NaN : dists[type].mean( ...parameters ) let min = dists[type].quantile(0, ...parameters ) if( min == -Infinity || min == Infinity){ min = dists[type].quantile(.01, ...parameters ) } let max = dists[type].quantile(1, ...parameters ) if( max == -Infinity || max == Infinity){ max = dists[type].quantile(.99, ...parameters ) } let xScale = d3.scaleLinear([0,1], [min,max]) let x, y let y1 = 0 for( let i=0; i<=n; i++){ x = xScale(i/n) y = dists[type].pdf( x , ...parameters ) if( y != -Infinity && y!= Infinity){ y1 = Math.max(y1, y) } dataFunction.push( ({x:x, y:y}) ) } dataMean = [({x1:mean, x2:mean, y1:y1*1.1, y2:0})] dataText = [ ({x:mean, y:y1*1.15, text:'True Mean'}) ] return Plot.plot({ height:200, width:width-20, marks: [ Plot.axisY({anchor: "left", tickSpacing: 35, label:'frequency'}), Plot.areaY(dataFunction, {x: "x", y: "y", fill:'steelblue', opacity:.2}), Plot.lineY(dataFunction, {x: "x", y: "y", stroke:'steelblue', opacity:1}), Plot.link(dataMean, {x1:'x1', x2:'x2', y1:'y1', y2:'y2', stroke:'black', strokeWidth:.5}), Plot.text(dataText, {x:'x', y:'y', text:'text'}), Plot.ruleY([0]) ] }) }31:T8ed,{ let runs = 20 let z = dists.normal.quantile( 1- (.5-option2[1]/200) , 0, 1) // two tailed let n = option2[0] let parameters = arg.find( e=> e.name == type ).arg let noMean = ['cauchy'] let actualMean = noMean.includes(type) ? NaN : dists[type].mean( ...parameters ) let min = dists[type].quantile(0, ...parameters ) if( min == -Infinity || min == Infinity){ min = dists[type].quantile(.01, ...parameters ) } let max = dists[type].quantile(1, ...parameters ) if( max == -Infinity || max == Infinity){ max = dists[type].quantile(.99, ...parameters ) } let dataPoints = [] let dataLine = [] let stdev, mean let a let x for( let j=0; jd.width==null?2:d.width}) ] }) }32:[] 2d:{"id":"64c3511b4bb3bfc6","slug":null,"title":"DDD#8 An illusion of predictability","thumbnail":"c44e9ced980ce7a89d4618d12e07c48a6bb20b51c324e034311d8716f0bb5839","access_level":"public","create_time":"$D2024-06-07T16:04:49.526Z","update_time":"$D2024-09-05T16:57:13.247Z","view_time":null,"first_public_time":"$D2026-05-21T04:40:03.915Z","fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"cf45be0120eccaad","login":"laotzunami","name":"Lao","avatar_url":"https://avatars-next.observableusercontent.com/aeddc181df6ca80a347940ba62e17601ac6395e9d2c21142887eca5fd277326a","tier":"starter_2024"},"version":577,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"5da1d0646b8496ac","login":"laotzunami","name":"Lao","avatar_url":"https://avatars-next.observableusercontent.com/9c14da488e1a68ca1868ed025eb7edcce3d300c8a9f3fbcdae66a3daa9ccca63","tier":null}],"members":[{"type":"individual","id":"5da1d0646b8496ac","login":"laotzunami","name":"Lao","avatar_url":"https://avatars-next.observableusercontent.com/9c14da488e1a68ca1868ed025eb7edcce3d300c8a9f3fbcdae66a3daa9ccca63","tier":null,"role":"editor"},{"type":"team","id":"cf45be0120eccaad","login":"laotzunami","name":"Lao","avatar_url":"https://avatars-next.observableusercontent.com/aeddc181df6ca80a347940ba62e17601ac6395e9d2c21142887eca5fd277326a","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"DDD#8 An illusion of predictability","cells":[{"id":0,"value":"# DDD#8 An illusion of predictability\n\n## Even experts confuse inferential uncertainty and outcome variability","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":5,"value":"Paper link:
[An illusion of predictability in scientific results:
Even experts confuse inferential uncertainty and outcome variability\n](https://www.pnas.org/doi/full/10.1073/pnas.2302491120)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":137,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":361,"value":"viewof type = Inputs.select( arg.map( e => e.name) , {value:'normal', label: \"Select a distribution\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":80,"value":"$30","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":374,"value":"viewof option2 = Inputs.form(\n [\n Object.assign(Inputs.range([0, 10000], {label: 'Samples per run', value:200, step: 1, transform: Math.log}),{style: '--label-width: 50px'}),\n Object.assign(Inputs.range([90, 99.9], {label: 'confidence range, %', value:95, step: .1}),{style: '--label-width: 65px'}),\n Inputs.button(\"Reroll sample\", {width:55})\n ],\n {\n template: (inputs) => htl.html`

\n ${inputs}\n

`\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":198,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":9,"value":"### Confidence Interval Equation\n\n${tex`CI = \\bar{x} \\pm z \\dfrac{s}{\\sqrt{n}}`}\n\nwhere:
\n${tex`\\bar{x} =`} sample mean
\n${tex`z =`} two tailed z score for confidence level
\n${tex`s =`} sample standard deviation
\n${tex`n =`} sample size
","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":566,"value":"| Cohen's d | Common Language Effect Size |\n|---|---|\n|0.2 | 53% |\n|0.5 | 58% |\n|0.8 | 62% |\n|2 | 75% |","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":563,"value":"CLES = { // cohen's d to common language effect size\n let d = 2\n let r = Math.sqrt(d**2 / (d**2 + 4))\n return Math.asin(r)/Math.PI+.5\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":447,"value":"### Libraries","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":31,"value":"stdlib = require( \"https://unpkg.com/@stdlib/stdlib@0.0.32/dist/stdlib-flat.min.js\" )","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":61,"value":"dists = stdlib.base.dists","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":365,"value":"[Form template notebook](https://observablehq.com/@tophtucker/use-inputs-form-with-a-template)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"}],"files":"$W32","stdlib":"1","titling":"auto"}} 2e:"$2d:body"